{
 "metadata": {
  "name": "Windowing_Part2"
 },
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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Introduction\n",
      "--------------\n",
      "\n",
      "In the last section, we used windows for spectral analysis and  noted that while windows helped distinguish weak signals buried in the sidelobes of nearby  stronger signals, there were many trade-offs involved. In this section, we put together the standard framework for analyzing and categorizing  windows. There are many, many windows used in signal processing, so we begin by considering the common characteristics of windows and then move on to developing the standard metrics for them."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Spectral Leakage\n",
      "\n",
      "Because computer memory is finite, we  must analyze a finite section of data. The key underlying assumption of the DFT is that the finite section is periodic with period $N_s$. When this actually turns out to be true, it is possible to exactly capture discrete frequencies. For example, given\n",
      "\n",
      "$$ x_n = \\sin \\left(\\frac{2\\pi f_o n }{f_s} \\right) $$\n",
      "\n",
      "with $ N_s = f_s/f_o = N$\n",
      "\n",
      "the following figure shows the effect of *spectral leakage*."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "from scipy import signal\n",
      "\n",
      "fo = 1 # signal frequency\n",
      "fs = 32 # sample frequency\n",
      "Ns = 32 # number of samples\n",
      "x = sin( 2*pi*fo/fs*arange(Ns)) # sampled signal\n",
      "fig,axs= subplots(3,2,sharex='col',sharey='col')\n",
      "fig.set_size_inches((12,6))\n",
      "subplots_adjust(hspace=.3)\n",
      "\n",
      "ax=axs[0,0]\n",
      "ax.plot(arange(Ns),x,label='signal')\n",
      "ax.plot(arange(Ns)+Ns,x,label='extension')\n",
      "ax.set_ylabel('Amplitude',fontsize=14)\n",
      "ax.set_title('Continuous at endpoints',fontsize=16)\n",
      "\n",
      "ax=axs[0,1]\n",
      "N=Ns  #chosen so DFT bin is exactly on fo\n",
      "Xm = abs(fft.fft(x,N))\n",
      "idx = int(fo/(fs/N))\n",
      "ax.stem(arange(N)/N*fs,Xm,basefmt='b-')\n",
      "ax.plot( fo, Xm[idx],'o')\n",
      "ax.set_ylabel(r'$|X_k|$',fontsize=18)\n",
      "ax.set_xlim(xmax = 5)\n",
      "ax.set_ylim(ymin=-1)\n",
      "ax.text(0.3,0.5,'No spectral leakage',fontsize=16,\n",
      "        transform=ax.transAxes,\n",
      "        bbox={'fc':'y','alpha':.3})\n",
      "ax.grid()\n",
      "\n",
      "# loss of continuity case\n",
      "\n",
      "fo = 1.1 # signal frequency\n",
      "x = sin( 2*pi*fo/fs*arange(Ns)) # sampled signal\n",
      "\n",
      "ax=axs[1,0]\n",
      "ax.plot(arange(Ns),x,label='signal')\n",
      "ax.plot(arange(Ns)+Ns,x,label='extension')\n",
      "ax.set_ylabel('Amplitude',fontsize=14)\n",
      "ax.set_title('Discontinuous at endpoints',fontsize=16)\n",
      "\n",
      "ax=axs[1,1]\n",
      "Xm = abs(fft.fft(x,N))\n",
      "idx = int(fo/(fs/N))\n",
      "ax.stem(arange(N)/N*fs,Xm,basefmt='b-')\n",
      "ax.plot( fo, Xm[idx],'o')\n",
      "ax.set_xlabel('Frequency(Hz)',fontsize=16)\n",
      "ax.set_ylabel(r'$|X_k|$',fontsize=18)\n",
      "ax.text(0.3,0.5,'Spectral Leakage',fontsize=16,\n",
      "        transform=ax.transAxes,\n",
      "        bbox={'fc':'y','alpha':.3})\n",
      "ax.set_xlim(xmax = 5)\n",
      "ax.set_ylim(ymin=-1)\n",
      "ax.grid()\n",
      "\n",
      "x = x*signal.triang(Ns,2)\n",
      "ax=axs[2,0]\n",
      "ax.plot(arange(Ns),x,label='signal')\n",
      "ax.plot(arange(Ns)+Ns,x,label='extension')\n",
      "ax.set_xlabel('sample index',fontsize=14)\n",
      "ax.set_ylabel('Amplitude',fontsize=14)\n",
      "ax.set_title('Window restores continuity at endpoints',fontsize=14)\n",
      "\n",
      "ax=axs[2,1]\n",
      "Xm = abs(fft.fft(x,N))\n",
      "idx = int(fo/(fs/N))\n",
      "ax.stem(arange(N)/N*fs,Xm,basefmt='b-')\n",
      "ax.plot( fo, Xm[idx],'o')\n",
      "ax.set_xlabel('Frequency(Hz)',fontsize=16)\n",
      "ax.set_ylabel(r'$|X_k|$',fontsize=18)\n",
      "ax.text(0.3,0.5,'Leakage with window',fontsize=16,\n",
      "        transform=ax.transAxes,\n",
      "        bbox={'fc':'y','alpha':.3})\n",
      "ax.set_xlim(xmax = 5)\n",
      "ax.set_ylim(ymin=-1)\n",
      "ax.grid()\n",
      "\n",
      "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
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YeqPr/UunTW2SYmtry19//ZWWKozi8WP1TpHffSd3JIb13XewaBE8eSJ3JOnX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hIAgwcP5tatW2zatEkt06pVq3j69KmqZfnRo0ccPnyYxo0bZ1uGjIwM0tPTs7zOr7dqT506lSNH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\ne3t75uDgwBwcHFhycrIgMxcUFDBHR0dmb2/PbG1t2dq1axljT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       "text": [
        "<matplotlib.figure.Figure at 0x5a7bab0>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the above figure, the top row shows the ideal situation where the sampling interval captures exactly one period of the signal and the DFT bin is exactly on the signal frequency. The DFT assumes that the section of the signal repeats            end-to-end with the sampling interval, implying no discontinuities at the joining ends. In practice, this never happens because we don't know the signal frequency ahead of time (if we did, there would be no point in spectral analysis!).\n",
      "\n",
      "The second row shows the case when the signal's period is *different* from the sampling interval and there is a discontinuity at the joining ends. When this happens, the DFT cannot perfectly isolate the signal's frequency and thus *leaks* energy into other frequency bins. This is known as *spectral leakage* and it causes bias in the frequency estimate.\n",
      "\n",
      "The third row shows using a window to reduce the discontinuity at edges. The corresponding DFT still exhibits spectral leakage so windows do not entirely cure this problem, but they do help in other ways. The remainder of this section explores the many ways to analyze windows and their effects and provides some guidelines for choosing windows in practice.\n",
      "\n",
      "The following figure shows how window functions affect the signal's power."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# some useful functions \n",
      "def dftmatrix(Nfft=32,N=None):\n",
      "    'construct DFT matrix'\n",
      "    k= np.arange(Nfft)\n",
      "    if N is None: N = Nfft\n",
      "    n = arange(N)\n",
      "    U = matrix(exp(1j* 2*pi/Nfft *k*n[:,None])) # use numpy broadcasting to create matrix\n",
      "    return U/sqrt(Nfft)\n",
      "\n",
      "def db20(W,Nfft=None):\n",
      "    'Given DFT, return power level in dB'\n",
      "    if Nfft is None: # assume W is DFT \n",
      "        return 20*log10(abs(W))\n",
      "    else: # assume time-domain passed, so need DFT\n",
      "        DFT= fft.fft(array(W).flatten(),Nfft)/sqrt(Nfft)\n",
      "        return 20*log10(abs(DFT.flatten()))\n",
      "\n",
      "U=dftmatrix(64) \n",
      "u=U[:,6].real*sqrt(2) # create test sinusoid\n",
      "fo = 2*pi/64*6 # in radians/sec\n",
      "nz=randn(64,1) # noise samples\n",
      "w=signal.triang(64) # window function\n",
      "\n",
      "fig,ax= subplots(2,1)\n",
      "fig.set_size_inches((10,5))\n",
      "subplots_adjust(hspace=.3)\n",
      "n = arange(len(u))\n",
      "ax[0].plot(n,u.real,label='before window',lw=2)\n",
      "ax[0].set_ylabel('Amplitude',fontsize=16)\n",
      "ax[0].plot(n,diag(w)*u.real,label='after window',lw=3.)\n",
      "ax[0].fill_between(n,array(u).flat, array(diag(w)*u).flat,alpha=0.3)\n",
      "ax[0].legend(loc=0,fontsize=12)\n",
      "ax[0].set_xlabel('n')\n",
      "ax[0].grid()\n",
      "ax[0].annotate('Lost signal due to window',fontsize=14, bbox={'fc':'b','alpha':.3},\n",
      "      xy=(11,0.1),\n",
      "      xytext=(30,40), textcoords='offset points',\n",
      "      arrowprops={'facecolor':'b','alpha':.3})\n",
      "\n",
      "N=256 # DFT size for plot\n",
      "idx = int(fo/(2*pi/N))\n",
      "ax[1].plot(db20(u,N),label='DFT before window')\n",
      "ax[1].plot(db20(diag(w)*u,N),label='DFT after window')\n",
      "ax[1].set_ylim(ymin=-40,ymax=-5)\n",
      "ax[1].set_xlim(xmax=40)\n",
      "ax[1].set_ylabel(r'$20\\log_{10}|X_k|$',fontsize=12)\n",
      "ax[1].set_xlabel(r'$k$',fontsize=14)\n",
      "ax[1].annotate('Loss of signal power',fontsize=14,xy=(22,-13),\n",
      "            xytext=(2,-15),\n",
      "            arrowprops={'facecolor':'m','alpha':.3})\n",
      "pkU = db20(u,N)[idx]\n",
      "pkW = db20(diag(w)*u,N)[idx]\n",
      "ax[1].annotate('',xy=(idx,pkW),xytext=(idx,pkU),fontsize=12,\n",
      "               arrowprops={'arrowstyle':'<->','color':'m'})\n",
      "ax[1].legend(loc=0,fontsize=12)\n",
      "ax[1].grid()\n",
      "\n",
      "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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wZp2dVgIp9Zeizpyo1Vm+nRqloigMHizD2FjFjh1yjh0r8uF6hy5mnlQqmDBB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uiTzfz587NmzRol2SxZsiQbN2585S1iYzCZT9/x48eze/duKleuzL59+xg/fjwAUVFRtGnTRtmv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\nrFQ13/Kk/IBKuYYsoaBCyWvL1jby0655OwxpPwTLjj5Z2sVcc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       "text": [
        "<matplotlib.figure.Figure at 0x739b8d0>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The figure above shows the loss in signal due to the window in the sample domain (top plot) and in the DFT-domain (bottom plot). The shaded region in the top plot shows the signal that has been eliminated due to the window, which slopes to zero away from the edges. The bottom plot shows the DFTs of the signal before and after windowing. As indicated, the loss in power is the drop in the DFT at the signal frequency, $f_o$. Note that the mainlobe of the windowed DFT is *much* larger than before which makes it harder to separate two nearby frequencies that are separated less than the width of the mainlobe. In general, losing signal power is not good, but we seldom consider the signal in isolation; rather, we always  regard  the signal in terms of its relationship to ever-present noise.\n",
      "\n",
      "### Signal-to-Noise Ratio\n",
      "\n",
      "To analyze the effect of windows, we define the signal-to-noise ratio and then compute it before and after applying the window function. For simplicity, we consider a perfect narrowband signal at frequency $f_o$ with amplitude, $ A $,\n",
      "\n",
      "$$ \\mathbf{x} = A \\mathbf{u}_o $$\n",
      "\n",
      "where \n",
      "\n",
      "$$ \\mathbf{u}_o =\\frac{1}{\\sqrt N_s} \\left[ \\exp \\left( j \\frac{2\\pi f_o }{f_s} n\\right) \\right]_{n=0}^{N_s-1}$$\n",
      "\n",
      "with signal power equal to $A^2$. We'll assume the noise power is $\\sigma_\\nu^2$. Thus, the pre-window signal-to-noise ratio is,\n",
      "\n",
      "$$ SNR_{pre} = \\frac{A^2}{\\sigma_\\nu^2}$$\n",
      "\n",
      "After applying the window, the updated signal power at $f=f_o$ becomes\n",
      "\n",
      "$$ \\DeclareMathOperator{\\diag}{diag}\n",
      "|\\mathbf{u}^H_o \\left(  \\mathbf{w} \\odot \\mathbf{x}  \\right)|^2= |\\mathbf{u}^H_o  \\diag (\\mathbf{w}) \\mathbf{x}|^2 = A^2 |\\mathbf{1}^T \\mathbf{w}|^2$$\n",
      "\n",
      "with corresponding noise power\n",
      "\n",
      "$$ \\DeclareMathOperator{\\Tr}{Trace}\n",
      "\\mathbb{E} | \\mathbf{w} \\odot \\mathbf{n} |^2 = \\Tr \\left( \\diag(\\mathbf{w}) \\mathbb{E} \\left(   \\mathbf{n}\\mathbf{n}^T \\right)\\diag(\\mathbf{w}) \\right) = \\Tr \\left(\\diag(\\mathbf{w}) \\sigma_\\nu^2 \\mathbf{I}\n",
      "\\diag(\\mathbf{w}) \\right) = \\sigma_\\nu^2 \\mathbf{w}^T \\mathbf{w}$$\n",
      "\n",
      "where $ \\mathbb{E}\\left( \\mathbf{n} \\mathbf{n}^T \\right)= \\sigma_\\nu^2 \\mathbf{I}$ and $\\mathbf{n}$ is a vector of mutually uncorrelated noise samples with variance $\\sigma_\\nu^2$.\n",
      "\n",
      "Thus the post-window signal-to-noise ratio is\n",
      "\n",
      "$$ SNR_{post} = \\frac{ A^2 |\\mathbf{1}^T \\mathbf{w}|^2}{\\sigma_\\nu^2 \\mathbf{w}^T \\mathbf{w}} $$\n",
      "\n",
      "Finally, the ratio of the post-window to pre-window  signal-to-noise ratios is defined as the *processing gain*,\n",
      "\n",
      "$$ G_p \\triangleq \\frac{SNR_{post}}{SNR_{pre}} = \\frac{ |\\mathbf{1}^T \\mathbf{w}|^2}{\\mathbf{w}^T \\mathbf{w}} $$\n",
      "\n",
      "Incidentally, the *coherent gain* is defined the ratio of the *amplitudes* of the input and output signals,\n",
      "\n",
      "$$ G_{coh} \\triangleq \\mathbf{1}^T \\mathbf{w}$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Thus, the window reduces signal power *and* noise power so the net effect is to increase the signal-to-noise ratio. Processing gain summarizes the effect. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Equivalent Noise Bandwidth\n",
      "\n",
      "Thus far, we have observed that the window can improve the signal-to-noise ratio because it reduces noise power less than it reduces signal power. However, this considers noise across the entire frequency domain and we want a metric to measure noise power around the mainlobe of the window's DFT. Then, we can think  about windows in terms of the amount of noise they *pass* through the mainlobe. The figure below illustrates this concept."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib.patches import Rectangle\n",
      "\n",
      "fig,ax = subplots()\n",
      "fig.set_size_inches((8,3))\n",
      "\n",
      "N = 256 # DFT size\n",
      "idx = int(fo/(2*pi/N))\n",
      "Xm = abs(fft.fft(array(diag(w)*u).flatten(),N)/sqrt(N))**2\n",
      "ax.plot(Xm,'-o')\n",
      "ax.add_patch(Rectangle((idx-10/2,0),width=10,height=Xm[idx],alpha=0.3))\n",
      "ax.set_xlim(xmax = N/4)\n",
      "ax.set_ylabel(r'$|W_k|^2$',fontsize=18)\n",
      "ax.set_xlabel(r'$k$',fontsize=18)\n",
      "ax.set_title('Equivalent Noise Bandwidth',fontsize=18)\n",
      "ax.annotate('Area of rectangle\\n is windowed\\nnoise power\\n'\\\n",
      "              +r'$\\sigma_\\nu^2 \\mathbf{w}^T \\mathbf{w}$',\n",
      "            fontsize=14,\n",
      "            xy=(idx,Xm.max()/2.),\n",
      "            xytext=(40,Xm.max()/2.),\n",
      "            arrowprops={'facecolor':'m','alpha':.3});\n",
      "ax.annotate('',ha='center',fontsize=24,\n",
      "             xy=(idx+10/2,Xm.max()*1.05),\n",
      "             xytext=(idx-10/2,Xm.max()*1.05),\n",
      "             arrowprops=dict(arrowstyle='<->'))\n",
      "ax.annotate('',ha='center',fontsize=24,\n",
      "             xy=(15,0),\n",
      "             xytext=(15,Xm.max()),\n",
      "             arrowprops=dict(arrowstyle='<->'))\n",
      "ax.text( 1, Xm.max()/2,r'$ |W_0|^2\\sigma_\\nu^2 $',fontsize=20,bbox={'fc':'gray','alpha':.3})\n",
      "ax.text( idx-5, Xm.max()*1.1,r'$B_{neq}$',fontsize=18,bbox={'fc':'gray','alpha':.3})\n",
      "ax.set_ylim(ymax = Xm.max()*1.2)\n",
      "ax.grid()\n",
      "\n",
      "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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hF+0IvWiiazrRaYMhIyODYcOGERISwvnz51m/fj1xcXFqdf7++28SEhKIj48n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\nEGBZV1enR7XcK2ojcXFO4uKopWPSqjs9CqFWX30FJhNERbm7JC2nXTs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       "text": [
        "<matplotlib.figure.Figure at 0x5481350>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The figure above shows the squared DFT of the window with the overlaid rectangle showing the idealized bandpass filter that would pass the same amount of noise power at the peak of the window's DFT. Thus, it's as if we gathered up all the noise power and centered it at the peak of the mainlobe. This is the *Equivalent Noise Bandwidth* (ENBW) concept. The post-window noise power is the following: \n",
      "\n",
      "$$\\mathbb{E} || \\mathbf{w} \\odot \\mathbf{n} ||^2 =  \\sigma_{\\nu}^2 \\mathbf{w}^T \\mathbf{w }$$\n",
      "\n",
      "We want to equate this power (which is spread over all frequencies) to the corresponding output noise power of a perfect bandlimited filter with height equal to $W_0$ and width $ B_{neq}$. \n",
      "\n",
      "$$   B_{neq} \\cdot W_0^2 \\sigma_\\nu^2 = \\sigma_{\\nu}^2 \\mathbf{w}^T \\mathbf{w } $$\n",
      "\n",
      "and solving for $B_{neq}$ gives,\n",
      "\n",
      "$$  B_{neq}  = \\mathbf{w}^T \\mathbf{w } / W_0^2   $$\n",
      "\n",
      "and since $W_0 = \\mathbf{1}^T \\mathbf{ w}$, we can write this as the following,\n",
      "\n",
      "$$  B_{neq}  \\triangleq \\frac{\\mathbf{w}^T \\mathbf{w } }{ |\\mathbf{1}^T \\mathbf{w}|^2 } =\\frac{1}{G_p} $$\n",
      "\n",
      "which shows how closely related this is to processing gain. The intuition here is that the larger the noise equivalent bandwidth, the more noise is passed through the mainlobe, thus competing more with the signal at the nominal center of the lobe, thus reducing the processing gain of the window.\n",
      "\n",
      "The following table reports the equivalent noise bandwidth for some popular windows normalized to the rectangular window's value. Note that the windows in `scipy` are available in `scipy.signal.windows`. The values in the table are match Harris' exhaustive 1978 paper using the matching `symmetry` argument in the Python call. See the corresponding window documentation for implementation details.\n",
      "\n",
      "<table border=\"1\">\n",
      "    <tr>\n",
      "    <th> Window </th>\n",
      "    <th>Python call</th>\n",
      "    <th> ENBW (bins) </th>\n",
      "    </tr>\n",
      "    <tr>\n",
      "        <td>rectangular</td><td style=\"font-family:monospace\">windows.boxcar(Ns)</td><td style=\"text-align:center\"> 1</td>\n",
      "    </tr>\n",
      "    <tr>\n",
      "        <td>triangular</td><td style=\"font-family:monospace\">windows.triang(Ns)</td><td style=\"text-align:center\"> 1.33</td>\n",
      "    </tr>\n",
      "    <tr>\n",
      "        <td>hamming</td><td style=\"font-family:monospace\">windows.hamming(Ns,sym=False)</td><td style=\"text-align:center\"> 1.36</td>\n",
      "    </tr>   \n",
      "    <tr>\n",
      "        <td>blackman</td><td style=\"font-family:monospace\">windows.blackman(Ns,sym=False)</td><td style=\"text-align:center\"> 1.73</td>\n",
      "    </tr>      \n",
      "</table> \n",
      "\n"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Summary"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this section, we explained the shape of windows functions in terms of spectral leakage and developed the concept of processing gain and equivalent noise bandwidth as closely related metrics for categorizing different window functions. The exhaustive 1978 paper by Harris (see references) is the primary reference work for many more windows functions than we discussed here. Note that the window functions are implemented in the `scipy.signal.windows` submodule but sometimes the normalization factors and defined parameters are slightly different from Harris' paper.  Sometimes the term *tapers* is used instead of *window functions* in certain applications. Lastly, window functions are also fundamental to antenna analysis for many of the same reasons, especially with respect to linear arrays.\n",
      "\n",
      "\n",
      "As usual, the corresponding IPython notebook for this post  is available for download [here](https://github.com/unpingco/Python-for-Signal-Processing/blob/master/Windowing_Part2.ipynb). \n",
      "\n",
      "Comments and corrections welcome!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "References\n",
      "---------------\n",
      "\n",
      "\n",
      "* Oppenheim, A. V., and A. S. Willsky. *Signals and Systems* Prentice-Hall, (1997).\n",
      "* Proakis, John G. *Digital signal processing: principles algorithms and applications* Pearson Education India, 2001.\n",
      "* Harris, Fredric J. \"On the use of windows for harmonic analysis with the discrete Fourier transform.\" Proceedings of the IEEE 66.1 (1978): 51-83."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}